Related papers: Completely inverse $AG^{**}$-groupoids
In the paper we study the algebroid A of the groupoid of partially invertible elements over the lattice of orthogonal projections of a $W^*$-algebra. In particular the complex analytic manifold structure of these objects is investigated.…
We define what it means for a proper continuous morphism between groupoids to be Haar system preserving, and show that such a morphism induces (via pullback) a *-morphism between the corresponding convolution algebras. We proceed to provide…
We adapt the abstract concepts of abelianness and centrality of universal algebra to the context of inverse semigroups. We characterize abelian and central congruences in terms of the corresponding congruence pairs. We relate centrality to…
In this paper we show that the universal C*-algebra satisfying the Cuntz-Li relations is generated by an inverse semigroup of partial isometries. We apply Exel's theory of tight representations to this inverse semigroup. We identify the…
We introduce a category of inverse semigroup actions and a category of \'etale groupoids. We show that there are three functors which send inverse semigroups to their spectral actions, inverse semigroup actions to their transformation…
We fix a path model for the space of filters of the inverse semigroup $\mathcal{S}_\Lambda$ associated to a left cancellative small category $\Lambda$. Then, we compute its tight groupoid, thus giving a representation of its $C^*$-algebra…
In this paper we present a novel algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. This algorithm uses a myriad of techniques from the theories of groups, automata, and inverse semigroups.…
In this note we start the study of whether the reduced C*-algebra of an inverse semigroup is quasi-diagonal, making explicit use of the inner structure of this class of semigroups in order to produce quasi-diagonal approximations. Given a…
A new subclass of AG-groupoids, so called, cyclic associative Abel-Grassman groupoids or CA-AG-groupoid is studied. These have been enumerated up to order $6$. A test for the verification of cyclic associativity for an arbitrary AG-groupoid…
We define a class of inverse monoids having the property that their lattices of principal ideals naturally form an MV-algebra. We say that an arbitrary MV-algebra can be co-ordinatized if it is isomorphic to one constructed in this way from…
An element $g$ in a group $G$ is called reversible if $g$ is conjugate to $g^{-1}$ in $ G $. An element $g$ in $G$ is strongly reversible if $ g $ is conjugate to $g^{-1}$ by an involution in $G$. The group of affine transformations of…
We develop a structural theory of chirality for inverse semigroups and show how it propagates canonically to \'{e}tale groupoids and twisted groupoid $C^*$-algebras. Starting from inverse semigroup data equipped with admissible twist…
Inspired by the work of Paterson on $C^{\ast}$-algebras of directed graphs, we show how to associate a groupoid $\mathfrak{G}_{\mathcal{G}}$ to an ultragraph $\mathcal{G}$ in such a way that the $C^*$-algebra of $\mathfrak{G}_{\mathcal{G}}$…
In this paper we have discusses {\Gamma}-left, {\Gamma}-right, {\Gamma}-bi-, {\Gamma}-quasi-, {\Gamma}-interior and {\Gamma}-ideals in {\Gamma}-AG^{**}-groupoids and regular {\Gamma}-AG^{**}-groupoids. Moreover we have proved that the set…
We investigate various groupoids associated to an arbitrary inverse semigroup with zero. We show that the groupoid of filters with respect to the natural partial order is isomorphic to the groupoid of germs arising from the standard action…
We give an algebraic characterisation of ordered groupoids, namely, we show that there is a categorical isomophism between the category of ordered groupoids and the category of $D$-inverse constellations. Here constellations are partial…
In this paper, we have discussed the properties of intuitionistic fuzzy ideals of an AG-groupoids. We have characterized an intra-regular AG-groupoid in terms of intuitionistic fuzzy left (right, two-sided) ideals, fuzzy (generalized)…
Groupoid actions on C*-bundles and inverse semigroup actions on C*-algebras are closely related when the groupoid is r-discrete.
Let G < SL(V) be a finite group, V is finite dimensional over a field F, p=char F and S(V) is the symmetric algebra of V. We determine when the subring of G-invariants S(V)^G is a polynomial ring. As a consequence, we classify, if F is…
Let A be a cogroup in the category of connected graded algebras over a commutative ring R. Let nu denote the inverse of A and chi the antipode of the underlying Hopf algebra of A. We clarify the differences and similarities of nu and chi,…